Frustration Networks

Competing interactions on graphs and the geometry of spin glass order

Frustrated edges: — / —
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40%
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Frustration arises when a network contains cycles where not all interaction constraints can be simultaneously satisfied. In a triangle with two ferromagnetic (+) and one antiferromagnetic (−) edge, at least one spin pair must violate its preferred alignment — the triangle is "frustrated."

Spin glasses are disordered magnets with random ferro- and antiferromagnetic couplings. Their energy landscape has exponentially many local minima separated by barriers. Blue edges are ferromagnetic (prefer aligned spins), red edges antiferromagnetic (prefer opposed). Frustrated edges glow orange.